Marginally trapped surfaces in spaces of oriented geodesics

Nikos Georgiou, Brendan Guilfoyle

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We investigate the geometric properties of marginally trapped surfaces (surfaces which have null mean curvature vector) in the spaces of oriented geodesics of Euclidean 3-space and hyperbolic 3-space, endowed with their canonical neutral Kaehler structures. We prove that every rank one surface in these four manifolds is marginally trapped. In the Euclidean case we show that Lagrangian rotationally symmetric sections are marginally trapped and construct an explicit family of marginally trapped Lagrangian tori. In the hyperbolic case we explore the relationship between marginally trapped and Weingarten surfaces, and construct examples of marginally trapped surfaces with various properties.

Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalJournal of Geometry and Physics
Publication statusPublished - Aug 2014
Externally publishedYes


  • Marginally trapped surface
  • Mean curvature
  • Neutral Kähler structure
  • Spaces of geodesics


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